PERTURBATION FINITE ELEMENT METHOD FOR SOLVING GEOMETRICALLY NONLINEAR PROBLEMS OF AXISYMMETRICAL SHELL

In analysing the geometrically nonlinear problem of an axisymmetrical thin-walled shell, the paper combines the perturbation method with the finite element method by introducing the former into the variational equation to obtain a series of linear equations of different orders and then solving the equations with the latter. It is well-known that the finite element method can be used to deal with difficult problems as in the case of structures with complicated shapes or boundary conditions, and the perturbation method can change the nonlinear problems into linear ones. Evidently the combination of the two methods will give an efficient solution to many difficult nonlinear problems and clear away some obstacles resulted from using any of the two methods solely. The paper derives all the formulas concerning an axisym-metric shell of large deformation by means of the perturbation finite element method and gives two numerical examples,the results of which show good convergence characteristics.     

螺旋槽管管内湍流流动与换热的三维数值模拟

利用Fluent对5种不同槽深的螺旋槽管进行了模拟求解,得出了湍流状态下螺旋槽管内流体的速度场和温度场,从微观上说明了螺旋槽管的强化传热机理。分析了槽深对螺旋槽管阻力性能和换热性能的影响。数值计算结果表明,该类螺旋槽管在湍流工况下的平均Nu数大约是光管的1.6—2.1倍,平均阻力系数f大约是光管1.5—4.5倍。与实验数据进行比较发现,数值模拟具有相当的可靠性。     

在材料非线性问题中的摄动有限元法

摄动法是解决非线性连续介质力学问题的一种有效方法.这种方法是建立在该问题的线性解析解的基础上的,因此,若得不到一个简单的解析解,应用这种方法去解决一些复杂的非线性问题将遇到困难.有限元法对解非线性问题也是一种十分有用的工具,然而一般来说,它需要相当长的计算时间. 本文介绍摄动有限元法.这种方法吸取上述两种方法的优点,能够解决更复杂的非线性问题,而且也能大量节省计算机的计算时间. 本文讨论了比例加载下的弹塑性力学问题,并提出一个带孔拉板的数值解.     

苯骈-15-冠-5-溴甲酚绿分光光度法测定钠

钠的分光光度测定方法很少。由于冠醚能和碱金属形成稳定的络合物,为分光光度测定钠展示了良好的前景,但到目前为止,利用冠醚分光光度测定碱金属仅集中在钾的测定方法方面,对于钠仅限于络合反应基础研究和分离方面的工作。根据钠的离子直径为1.90A,我们选择了冠醚孔穴直径为1.7到2.2的苯骈-15-冠-5,并配以溴甲酚绿,它们和钠形     

THE PERTURBATION FINITE ELEMENT METHOD FOR SOLVING PROBLEMS WITH NONLINEAR MATERIALS

The perturbation method is one of the effective methods for so-lving problems in nonlinear continuum mechanics.It has been de-veloped on the basis of the linear analytical solutions for the o-riginal problems.If a simple analytical solution cannot be ob-tained.we would encounter difficulties in applying this method tosolving certain complicated nonlinear problems.The finite ele-ment method appears to be in its turn a very useful means for sol-ving nonlinear problems,but generally it takes too much time incomputation.In the present paper a mixed approach,namely,theperturbation finite element method,is introduced,which incorpo-rates the advantages of the two above-mentioned methods and enablesus to solve more complicated nonlinear problems with great savingin computing time.Problems in the elastoplastic region have been discussed anda numerical solution for a plate with a central hole under tensionis given in this paper.     

摄动有限元法解一般轴对称壳几何非线性问题

本文在处理几何非线性问题时,利用在变分方程中引入振动过程,得到各级变分摄动方程,并通过有限元法求解。由于有限元法能成功地处理各种复杂边界条件、几何形状的力学问题,摄动法又可将非线性问题转化为线性问题求解。若结合这两种方法的优点,将能够解决大量复杂的非线性力学问题。并能够消除单独使用有限元法或摄动法求解复杂非线性问题所出现的困难。 本文应用摄动有限元法求解了一般轴对称壳的几何非线性问题。